Babylonian Algebra from “Crest of the Peacock"

 

                        Source: https://www.goodreads.com/book/show/2189976.Babylonians

Table 4.2 in the reading “Babylonian algebra” surprised me that how peoples used words to represents quantities in ancient time when algebraic notations were not discovered. I noticed the word problems in the reading are related to fields and measurement. I think the words such as “ush”, “sag”, “lagab”, “sukud”, “asha”, “sahar” reflects their everyday lifestyle and culture. They used these kinds of words to solve math problems in their daily lives. It also tells us that in math, real-world issues play an essential role. In modern word problems, we also use words and number that represent our background and knowledge. For example: When we tell students to come up with an expression for “The sum of two numbers is equal to fifteen”, they know the meaning of “sum”, and they also know that a number should have a value.

           I believe that generalization and abstraction both play a significant role in developing mathematical knowledge. The tangible things can turn into abstraction, which helps to generalize the idea of mathematics. Generalization and abstraction help students to understand the concept behind what they are learning. For example: During my volunteer experience, a teacher used different sizes of cereal and cookie boxes to teach nets and surface area of the rectangular prisms. Using this approach, students can form their generalization to understand the concept.

           I think imagining geometry or graph theory without algebra is reasonable because these require visual representation to solve the problem. But calculus without algebra seems a bad nightmare for me. For example: in the question “2x – 400 = 244”, students can quickly find the number (x) by using algebraic steps. But if the problem is “How old am I if 400 reduced by two times my age is 244?” they will struggle with the words in the first place, and maybe they come up with the wrong equation that will give the wrong answer as well.